At a time when Tony Blair is backtracking on the issue, the shopworkers' union Usdaw has tabled a motion expressly demanding that delegates confirm that a strict formula should be imposed.
It is known that party leaders want to abandon the policy which commits a future Labour government to introducing a minimum wage tied to half male median earnings.
Mr Blair and his senior colleagues are thought to remain in favour of the principle of a statutory minimum wage, but unhappy that a future Labour Cabinet should have to deal with a highly prescriptive party policy.
The Transport and General Workers' Union, Labour's largest affiliate and the party's biggest financial backer, has tabled a similar proposition.
While unions at the TUC were persuaded to delete from their motion the figure of pounds 4 an hour - the present level of the formula - they insisted that the earnings floor should be tied to male earnings. The TUC resolution states that the minimum should be gradually uprated to two-thirds of average earnings. This has been Labour Party policy since being adopted at its conference eight years ago.